An intermediate stage in Hrushovski’s construction of flat strongly minimal structures in a relational language L produces ω-stable structures of rank ω. We analyze the pregeometries given by forking on the regular type of rank ω in these structures. We show that varying L can affect the isomorphism type of the pregeometry, but not its finite subpregeometries. A sequel will compare these to the pregeometries of the strongly minimal structures.

We prove that a simple theory of SU-rank 1 is n-ample if and only if the associated theory equipped with a predicate for an independent dense subset is n-ample for n at least 2.